The work described here is a first step towards the study of crossing equations, only enabling for their formulation in a large variety of cases. Some remarkable progress in understanding the structure of solutions, and thereby conformal field theories, was made in recent years by considerations of the simplest correlator of identical scalar fields \(\langle \varphi \varphi \varphi \varphi \rangle \) , [1]}, [2]}, [3]}, [4]}. It should be possible to obtain much more information by studying crossing for various types of fields. In the concluding Section , we will comment on the future developments in this direction that we hope our results may lead to.
